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We derive a priori error estimates for Nitsche's method applied to elliptic problems on approximate domains. Such approximations arise, for example, in unfitted finite element methods, data-driven simulations, and evolving domain problems,…
Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…
Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
We study two fundamental problems dealing with curves in the plane, namely, the nearest-neighbor problem and the center problem. Let $\mathcal{C}$ be a set of $n$ polygonal curves, each of size $m$. In the nearest-neighbor problem, the goal…
We address the problem of camera-to-laser-scanner calibration using a checkerboard and multiple image-laser scan pairs. Distinguishing which laser points measure the checkerboard and which lie on the background is essential to any such…
Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…
Lane detection is typically tackled with a two-step pipeline in which a segmentation mask of the lane markings is predicted first, and a lane line model (like a parabola or spline) is fitted to the post-processed mask next. The problem with…
We extend decision tree and random forest algorithms to product space manifolds: Cartesian products of Euclidean, hyperspherical, and hyperbolic manifolds. Such spaces have extremely expressive geometries capable of representing many…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space, and a query point (image),…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
Given the necessity of connecting the unconnected, covering blind spots has emerged as a critical task in the next-generation wireless communication network. A direct solution involves obtaining a coverage manifold that visually showcases…
A change point problem occurs in many statistical applications. If there exist change points in a model, it is harmful to make a statistical analysis without any consideration of the existence of the change points and the results derived…
A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
This paper considers metric spaces where distances between a pair of nodes are represented by distance intervals. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a…